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On Shimura’s trace formula

Published online by Cambridge University Press:  22 January 2016

Shinji Niwa
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In [1], G. Shimura gave a very practical formula of the traces of the Hecke operators acting on the space of cusp forms of rational weight and there he emphasized that the traces are effectively computable. We shall practice the computation in some special cases and discuss the structure of the Hecke algebra, which is not necessarily semi-simple.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 66 , May 1977 , pp. 183 - 202
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1977

References

[1] Shimura, G., On the trace formula for Hecke operators, Acta Math., 132 (1974), 245–128.CrossRefGoogle Scholar
[2] Shimura, G., On modular forms of half integral weight, Ann. of Math., 97 (1973), 440–481.Google Scholar
[3] Shimura, G., Publications of Math. Soc. Japan, no. 11, 1971.Google Scholar
[4] Hijikata, H., Explicit formula of the traces of Hecke operators for Γ0(N) , J. Math. Soc. Japan, Vol. 26, No. 1 (1974), 56–82.Google Scholar
[5] Yamauchi, M., On the traces of Hecke operators for a normalizer of Γ0(N) , J. Math. Kyoto Univ., 13 (1973), 403–411.Google Scholar
[6] Kubota, T., On a classical theta-function, Nagoya Math. J., Vol. 37 (1970), 183–189.Google Scholar
[7] Saito, H., Automorphic forms and algebraic extensions of number fields, Lecture note in Mathematics, Kyoto University (1975).Google Scholar
[8] Shintani, T., On construction of holomorphic cusp forms of half integral weight, Nagoya Math. J., Vol. 58 (1975), 83–126.CrossRefGoogle Scholar
[9] Ihara, Y., Hecke polynomials as congruence ζ functions in elliptic modular case, Ann. of Math., 85 (1967), 267–295.Google Scholar